# What is the vertex form of 2y=5x^2+4x+1 ?

Mar 3, 2017

The vertex form is $y = \frac{5}{2} {\left(x + \frac{2}{5}\right)}^{2} + \frac{1}{10}$

#### Explanation:

We perform this by completing the squares

$2 y = 5 {x}^{2} + 4 x + 1$

$y = \frac{5}{2} {x}^{2} + 2 x + \frac{1}{2}$

$y = \frac{5}{2} \left({x}^{2} + \frac{4}{5} x\right) + \frac{1}{2}$

$y = \frac{5}{2} \left({x}^{2} + \frac{4}{5} x + \frac{4}{25}\right) + \frac{1}{2} - \frac{2}{5}$

$y = \frac{5}{2} {\left(x + \frac{2}{5}\right)}^{2} + \frac{1}{10}$

This is the vertex form of the equation